Electricity generation using wind power ( TQL)

2.1, for example, an automobile is shown as having an efficiency of about 25% and has a power rating of about 0.3× 106W, which is roughly equivalent to 400 HP.1 2.2 Theoretical Power Ava

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I

ELECTR1C1TY GENERAT10N

US1NG W1ND POWER

.world

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WIND POWER

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N E W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • TA I P E I • C H E N N A I

World Scientific

ELECTRICITY GENERATION

USING WIND POWER

William Shepherd

University of Bradford, UK

Li Zhang

University of Leeds, UK

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British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA In this case permission to photocopy is not required from the publisher.

Desk Editor: Tjan Kwang Wei

Published by

World Scientific Publishing Co Pte Ltd.

5 Toh Tuck Link, Singapore 596224

USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

Printed in Singapore.

ELECTRICITY GENERATION USING WIND POWER

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Foreword and Acknowledgement

This book is written for electrical engineers and students of electrical neering As a textbook it is pitched at the level of final-year undergraduatesand postgraduates There is no detailed coverage of the aeronautical andmeteorological features of wind turbines The book is not intended as adesign handbook Certain of the chapters contain end-of-chapter numericalproblems, with the answers shown separately at the end of the book Some

engi-of the material in chapters 2, 5, 6 and 7 is reworked from earlier publications

by of one of the authors (WS) This material is acknowledged in appropriateplaces and the authors are grateful to the publishers of the earlier work fortheir permission to reproduce it

Bradford, England

2010

v

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This page is intentionally left blank

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Foreword and Acknowledgement v

1 The Development of Wind Converters 1 1.1 Nature and Origin of the Wind 1

1.2 Development of Wind Converters 3

References 6

2 Theory of Wind Converters 7 2.1 Power and Energy Basis of Wind Converters 7

2.1.1 Origin and properties of the wind 7

2.1.2 Power and energy 8

2.2 Theoretical Power Available in the Wind 9

2.3 Theoretical Maximum Power Extractable from the Wind 11

2.4 Practical Power Extractable from the Wind 15

2.4.1 Power coefficient 15

2.4.2 Torque versus rotational speed 16

2.4.3 Shaft power versus rotational speed 16

2.4.4 Tip-speed ratio (TSR) 17

2.5 Mechanical Features of Wind Machines 19

2.5.1 Axial thrust (Pressure) 19

2.5.2 The “Yaw” effect 20

2.5.3 Gyroscopic forces and vibrations 20

2.5.4 Centrifugal forces 22

2.5.5 Solidity factor 22

vii

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2.5.6 Two rotor blades or three rotor blades? 23

2.5.7 Shaft torque and power 24

2.6 Fixed Rotational Speed or Variable Rotational Speed? 26

2.6.1 Constant speed operation 27

2.6.2 Variable speed operation 28

2.7 Efficiency Considerations of Wind-Powered Electricity Generation 29

2.8 Worked Numerical Examples on Wind-Turbine Operation 31

2.9 Problems and Review Questions 36

References 38

3 Past and Present Wind-Energy Turbines 41 3.1 Nineteenth-Century Windmills 41

3.2 Early Twentieth-Century Wind-Energy Turbines 43

3.3 Later Twentieth-Century Wind-Energy Turbines 48

3.4 Modern Large Wind Power Installations 51

3.5 Worked Numerical Example 59

3.6 Vertical Axis Wind Machines 60

3.6.1 The Savonius design 61

3.6.2 The Darrieus design 62

3.6.3 Other forms of vertical axis machine 63

References 63

4 The Location and Siting of Wind Turbines 65 4.1 The Availability of Wind Supply 65

4.1.1 Global survey 65

4.1.2 Energy content of the wind 66

4.1.3 Wind-energy supply in Europe 68

4.1.4 Wind-energy supply in the USA 74

4.2 Statistical Representation of Wind Speed 79

4.3 Choice of Wind Turbine Sites 84

4.3.1 Identification of suitable areas 85

4.3.2 Selection of possible sites within the chosen area 85

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4.4 Effects of the Site Terrain 87

4.5 Spacing Effects of Wind Farm Arrays 89

References 92

5 Power Flow in Electrical Transmission and Distribution Systems 93 5.1 Basic Forms of Power Transmission Networks 93

5.2 Current and Voltage Relationships 95

5.3 Power Relationships in Sinusoidal Circuits 99

5.3.1 Instantaneous power 99

5.3.2 Average power and apparent power 100

5.3.3 Power factor 101

5.3.4 Reactive power 103

5.4 Complex Power 105

5.5 Real Power Flow and Reactive Power Flow in Electrical Power Systems 109

5.5.1 General summary 109

5.5.2 Summary from the perspective of the consumer 111

References 111

6 Electrical Generator Machines in Wind-Energy Systems 113 6.1 DC Generators 113

6.2 AC Generators 114

6.3 Synchronous Machine Generators 114

6.4 Three-Phase Induction Machine 121

6.4.1 Three-phase induction motor 122

6.4.2 Three-phase induction generator 127

6.4.3 Different generation systems 132

6.5 Analysis of Induction Generator in Terms of Complex Vector Representation 136

6.5.1 Three-phase to d-q-0 space vector transformation 140

6.6 Switched Reluctance Machines 143

6.6.1 Switched reluctance motors 143

6.6.2 Switched reluctance generator 144

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6.7 What Form of Generator is the Best Choice

for Wind Generation Systems? 145

References 146

7 Power Electronic Converters in Wind-Energy Systems 147 7.1 Types of Semiconductor Switching Converters 147

7.2 Three-Phase Controlled Bridge Rectifier 148

7.3 Three-Phase Controlled Bridge Inverter Feeding an Infinite Bus 154

7.3.1 Output voltage 154

7.3.2 Real (average) power output 158

7.3.3 Reactive power 159

7.3.4 RMS output current 160

7.3.5 Inverter power factor 162

7.4 The Effect of AC System Reactance on Inverter Operation 164

7.5 Three-Phase Cycloconverter Feeding an Infinite Bus 165

7.6 Matrix Converter Feeding an Infinite Bus 166

7.7 Worked Numerical Examples 169

7.7.1 Three-phase bridge rectifier 169

7.7.2 Three-phase bridge inverter feeding on infinite bus 170

7.8 Commonly Used Forms of Power Electronic Drive in Wind-Energy Systems 175

7.8.1 Fixed-speed and directly coupled cage induction generator 175

7.8.2 Variable-speed and doubly fed induction generator 176

7.8.3 Variable-speed and direct drive synchronous generator 177

7.9.1 Three-phase controlled bridge rectifier, with ideal supply, feeding a highly inductive load 178

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7.9.2 Three-phase, full-wave, and controlled bridge

inverter feeding an infinite bus 179

References 180

8 Integrating Wind Power Generation into an Electrical Power System 181 8.1 Electricity Distribution Systems 182

8.2 Issues for Consideration Concerning the Integration of Wind-Energy Generation into an Electric Power System 183

8.2.1 Energy credit 184

8.2.2 Capacity credit 187

8.2.3 Control and reliability 188

8.3 The Effect of Integrated Wind Generation on Steady-State System Voltages 190

8.4 The Effect of Integrated Wind Generation on Dynamic and Transient System Voltages 193

8.4.1 Lightning strikes 194

8.4.2 Voltage flicker 194

8.4.3 Harmonics 195

8.4.4 Self-excitation of induction generators 200

References 201

9 Environmental Aspects of Wind Energy 203 9.1 Reduction of Emissions 203

9.1.1 World consumption of coal 203

9.1.2 Open coal fires 205

9.2 Effluents due to Coal Burning 206

9.2.1 Sulphur oxides 206

9.2.2 Nitrogen oxides 207

9.2.3 Particulates 208

9.2.4 Carbon dioxide 209

9.3 Wind Turbine Noise 209

9.3.1 Measurement of wind turbine aerodynamic noise 212

9.3.2 Mechanical noise 214

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9.4 Electromagnetic Interference from Wind Turbines 215

9.4.1 Electromagnetic interference radiated from wind turbines 215

9.4.2 Electromagnetic interference effects due to the rotating blades 216

9.5 Effect of a Wind Turbine on Wildlife 217

9.6 Visual Impact of Wind Turbines 219

9.6.1 Individual response 219

9.6.2 Shadow flicker 219

9.7 Safety Aspects of Wind-Turbine Operation 220

References 220

10 Economic Aspects of Wind Power 223 10.1 Investment Aspects of Wind-Powered Electricity Generation 223

10.1.1 Costs of the turbines and generators 224

10.1.2 Costs of the turbine site, construction, and grid connection 225

10.1.3 Operation and maintenance (O and M) costs 226

10.1.4 Turbine lifetime and depreciation rate 227

10.1.5 Cost associated with the financing of wind farm building and operation 228

10.1.6 Wind regime at the turbine site 229

10.2 Comparative Costs of Generating Electricity from Different Fuel Sources 230

References 234

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C H A P T E R 1

The Development of Wind Converters

1.1 Nature and Origin of the Wind

The wind is the motion of a mass of air For the purpose of using wind energy,

it is normally the horizontal component of the wind that is of interest There

is also a vertical component of the wind that is very small compared with thehorizontal component, except in local disturbances such as thunderstormupdrafts

At the earth surface, the atmospheric pressure is measured in the unitPascal (Pa) and has an average value 101,325 Pa, which is sometimes called

“one atmosphere” Another unit of pressure used for meteorological tions is the millibar (mbar) There are exactly 100 Pa per millibar so that oneatmosphere is about 1,000 mbar On a map, regions of equal atmosphericpressure are identified by isobar lines such as those illustrated in Fig 1.1

calcula-A close concentration of isobar lines indicates a high pressure gradient orregion of rapid pressure change Wind speed is directly proportional to thepressure gradient

The atmospheric pressure varies from place-to-place and from day, caused by the combined effects of solar heating and the rotation ofthe earth As the earth spins, illustrated in Fig 1.2, the atmospheric air

day-to-1

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2 Electricity Generation Using Wind Power

Fig 1.1 Atmospheric pressure isobars for North America, April 2008 [1].

Fig 1.2 The Coriolis effect on wind direction [1].

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surrounding it is dragged round with it at different levels depending onaltitude The mix of air forms turbulence causing wind at the earth surface.

An additional feature is the inertial force known as the Coriolis force,which occurs in rotational systems When air moves over the surface of theearth as it rotates, instead of travelling in a straight line, the path of themoving air veers to the right The effect is that air moving from an area

of higher pressure to an area of lower pressure moves almost parallel tothe isobars In the northern hemisphere, the wind circles in a clockwisedirection towards the area of low pressure but in the southern hemisphere,the wind circles in an anti-clockwise direction, as shown in Fig 1.2

The heating effect of solar radiation varies with latitude and with the time

of day The warming effect is greater over the equator causing less densewarmer air to rise above the cooler air, reducing the surface atmosphericpressure compared with the polar regions The combined effect of the solarheating and the Coriolis force is to create the following prevailing winddirections[1]

1.2 Development of Wind Converters

Wind energy provided the motive power for sailing ships for thousands ofyears, until the age of steam The fortunes of the European colonial powerssuch as England, France, Germany, Spain, Portugal, Holland and Belgiumrested on their mastery of the sea and its navigation But the intermittentnature and uncertain availability of the wind combined with the relativeslowness of wind powered vessels gradually gave way to fossil-fuel poweredcommercial shipping Today, most shipping uses oil fuelled diesel engines

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Fig 1.3 Global wind distribution [1].

However, yachting and small boat sailing remain important recreationalsports throughout the world

The wind has also been used for thousands of years to provide the motivepower for machines acting as water pumps or used to mill or grind grain.Such machines came to be known as “windmills” The operators of wind-mills in feudal England took the name of their craft and acquired the surnameMiller (or Millar)

Very early wind machines were vertical axis structures and have beenidentified in China, India, Afghanistan and the Middle East, especiallyPersia, going back to about 250 B.C and possibly much earlier

Horizontal axis wind machines were developed by the Arab nations andtheir use became widespread throughout the Islamic World In Europe, thehorizontal axis wind machine became established about the 11th CenturyA.D., mostly having the form of a tower and rotating sails which becameknown as the Dutch windmill The earliest recorded windmill dates from

1191 A.D By the 18th Century A.D., multi-sail Dutch windmills wereextensively used in Europe It is estimated that by 1750 A.D there were

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Fig 1.4 Classical ‘Dutch’ windmill in Southern England (unknown origin).

8,000 windmills in operation in Holland and about 10,000 windmills inboth Britain and Germany Dutch settlers built windmills in North America,mainly along the eastern coast areas that became the New England states

of the USA At one stage, the shore of Manhattan Island was lined withwindmills built by Dutch settlers[2]

The principal features of the classical type of Dutch windmill are trated in Fig 1.4 Usually there are four sails, located upstream (i.e., facinginto the wind) Five, six and eight mills have been built Although a five-sailed machine is relatively efficient, it is disabled by the failure of just one

illus-of its blades On the other hand, a six-sailed machine can continue to ate with four, three or two sails, if necessary One of the many engineeringsketches left by Leonardo da Vinci (1452–1519 A.D.) represents a designfor a six-sailed windmill[3]

oper-To achieve variation of the rotational speed, the effective sail area of aDutch type of windmill can be modified by the use of shutters This corre-sponds to furling the sails on a yacht Furling or shuttering can also be used

to prevent over-speeding in high wind conditions The cupola on top of thetower, in Fig 1.4 for example, is designed to rotate, under the guidance of

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a rudder or stabilizer wheel, so that the sails remain upstream and dicular to the wind direction Mechanical rotational power obtained fromthe sail shaft is transmitted down the tower, via a beveled toothed bearing,onto a vertical drive shaft This, in turn, drives a toothed gear system whichsupplies power to rotate a grinding wheel for the corn

perpen-In Fig 1.4, the height of the horizontal, rotating axis above the ground

is often called the “hub height” For a typical windmill this might be 30 ft,

40 ft or even 50 ft high Despite such a large structure the power rating

of this Dutch windmill is the mechanical equivalent of only a few tens

of kilowatts The power developed by such a large structure is thereforeroughly equivalent to the electrical power supply now required by a largefamily house in Western Europe or North America In engineering terms,the efficiency of a Dutch windmill is low, although this may be a secondaryconsideration since the input power is free

Wind energy is transmitted by what is essentially a low density fluid.(i.e., the wind) The physical dimensions of any device used to convertits kinetic energy into a usable form are necessarily large in relation to thepower produced Wind availability is not only intermittent but unpredictable.The energy source, however, is free, environmentally clean and infinitelyrenewable There is no pollution and no direct use of fossil fuels in theenergy gathering process

References

1 “Wind Energy and Wind Power”, Solcomhouse website, Oct 2008, http://www solcomhouse.com/windpower.htm

2 McVeigh, J C., Energy Around the World, Pergamon Press, Oxford, England, 1984.

3 Golding, E W The Generation of Electricity by Wind Power Chapter 2 “The History

of Windmills”, E and F N Spon Ltd., London, England, 1955.

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C H A P T E R 2

Theory of Wind Converters

2.1 Power and Energy Basis of Wind Converters

2.1.1 Origin and properties of the wind

From the viewpoint of energy conversion, the most important properties ofthe wind at a particular location are the velocity of the airstream and the airdensity The air density varies with altitude and with atmospheric conditionssuch as temperature, pressure, and humidity At sea level and at standardatmospheric temperature and pressure, the value is:

ρ = 1.201 kg/m3at 1,000 millibars (29.53 inches of mercury) or

101.3 kilo pascal (kPa) pressure and temperature 293 K.

In the UK, a useful figure for the atmospheric air density is:

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the air decrease with altitude For wind-turbine applications, the range ofinterest is mostly within a couple of hundred feet of ground level Withinthis range, it is adequate to use the density values in Eqs (2.1) and (2.2) ortheir local alternatives at other locations

2.1.2 Power and energy

It is important to note that power P and energy W are not the same thing.

The energy of a system is its capacity for doing work, irrespective of thetime taken to do it The power of a system is the time rate of doing work

or expending energy and therefore has the dimension of energy (or work)divided by time

Power= Energy (Work)

In most wind-energy calculations, the average power in Eq (2.4) is used

In the Systeme Internationale (S.I.) system of units used in this book, theunit of energy is the joule and the unit of power is the joule per sec (J/s),which is usually called the watt (W) For practical engineering purposes, it isoften more convenient to use the kilowatt (kW) or megawatt (MW) A table

of conversion factors relating power and energy is given as Table 2.1

Power in watts is not concerned exclusively with electrical engineering.For example, the rotational mechanical power of engines is often expressed

in kilowatts The power ratings in watts of various devices and animals areshown in Fig 2.1, using a logarithmic scale.1

In terms of the human perception of power, it is sometimes helpful touse the old British power unit of horsepower (HP)

Energy converters with a rotational mechanical output, such as combustionengines and wind turbines, can be rated either in the mechanical units of

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Table 2.1 Conversion factors in power and energy.

1 kilowatt hour (kWh) 3.6 × 10 6 Joules

1 megawatt hour (MWh) 3.6 × 10 9 Joules

Atmospheric Pressure = 14.7 psi 101.325 kPa

horsepower or in the electrical units of kilowatts From Fig 2.1, for example,

an automobile is shown as having an efficiency of about 25% and has a power

rating of about 0.3× 106W, which is roughly equivalent to 400 HP.1

2.2 Theoretical Power Available in the Wind 1

If the air mass is m and it moves smoothly with an average velocity V , the

motion of the air mass has a kinetic energy (KE)

KE= 1

2mV

2

Consider a smooth and laminar flow of wind passing perpendicularly

(normally) through an element of area A of any shape, having thickness

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Fig 2.1 Efficiencies of energy converters.1

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Table 2.2 Power available in the wind3(at standard temperature and pressure).

Power Swept area, A Wind velocity, V Power equation, P w

It is seen that RHS of Eq (2.9) represents a force (1/2)ρAV2 multiplied

by a distance x Now, the KE passing through the element per unit time is

equal to the power rating:

Table 2.2 summarises more detailed expressions for the power in watts

in English units and in metric units

2.3 Theoretical Maximum Power Extractable

from the Wind 1,2

Only a fraction of the total theoretical power available in the wind, sented by Eq (2.12), is extractable It is an intrinsic property of all phys-ical systems that when energy is converted from one form to another, thisconversion is accompanied by various energy losses The result is that con-version is always subject to significant intrinsic limitations of efficiency

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Fig 2.2 Element of space through which the air flow passes.1

Fig 2.3 Rotor of a wind converter.1

Let a flow of smooth and steady air with an upstream average velocity

V1 impinge upon the rotor of a wind machine, as illustrated in Fig 2.3.Some of the energy from the wind is transferred to the wind machine rotor

so that the smooth and steady air far downstream flows at a smaller average

velocity V2 The KE reduction of the airflow, of mass m, per unit time is:

Kinetic Energy (KE)= 1

= 1

2m

V12− V2 2

In the process of extracting energy from the wind, the wind velocity Vrthat

actuates the rotor is less than the upstream “free wind” velocity V1 With

an ideal and lossless system, all of the energy reduction in the airstream

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is transferred to the rotor of the wind machine The downstream average

velocity V2is then smaller than the actuating velocity Vrat the rotor

Combining Eq (2.8) with Eq (2.11) for the airstream at the rotor bladesgives an expression for the time rate of air mass transferred

dm dt

V12− V2 2

there-Substituting for Vr from Eq (2.19) into Eq (2.16) gives an expression for

the power extractable from the wind by the rotor Using the symbol Pextodenote extracted power,

Pex= 1

4ρA(V1+ V2)

V12− V2 2

= 1

4ρAV

3 1

The value of wind velocity ratio V2/V1 that results in maximum power

transfer is calculated by differentiating Eq (2.20) with respect to (V /V )

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and equating to zero This results in a quadratic equation showing that to

maximise Pexthe ratio V2/V1must have the values either V2/V1= 1/3 or

1

2ρAV

3 1

Table 2.3 shows the values of the maximum theoretical power obtainablefrom a range of wind-turbine sizes at typical wind speeds.3It is notable howlarge a circular area must be used to generate any useful amount of power.For example, in a 10-mph wind, which is a light breeze, a swept area of

25 ft diameter would realise only a maximum theoretical value of 1.5 kW(and a practical value of roughly one-half of that) This immediately pointsTable 2.3 Maximum theoretical power extractable by ideal wind machine3

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to the difficulty of using wind energy for domestic use in urban areas—theswept area required is too large to be practicable.

Wind speed is usually expressed in miles per hour (mph) but also often

in metric units of metre/second (m/s) It is useful to use the conversionfactor:

eter called the power coefficient Cp With an upstream velocity V1, the

extractable power Pexcan be written as:

Coefficient Cpis seen to be the ratio of the power Pwin the wind (2.12) and

the power Pexextracted (2.24) It therefore represents the efficiency of theturbine rotor:

Cp= Pex

PW

= turbine rotor efficiency. (2.25)

Parameter Cpis a dimensionless variable By comparison of Eq (2.24) with

Eq (2.20), it is seen that Cpcan be expressed in terms of the upstream anddownstream average wind speeds

Cp= 12

example, the power available from the wind is 0.4/0.593 or about 67% of

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the ideal theoretical value and is 40% of the total power in the wind Power

coefficient Cp has a value that depends on the wind average velocity, theturbine rotational velocity and also on turbine blade design parameters such

as the pitch angle

2.4.2 Torque versus rotational speed

The basic operating characteristic for any rotational mechanical machine

is the shaft torque T versus the shaft rotational speed ω A separate T -ω

characteristic is obtained for each different value of wind speed at the bine rotor Typical forms of characteristic are shown in Fig 2.4 for two wind

tur-speeds Vand V, where V > V The value of the torque at zero speed

is the starting or stall torque, caused by friction, which has to be overcomebefore rotation will commence Stall torque increases, for any wind turbine,

as the wind velocity V increases The locus of the maximum torque values

Tmin Fig 2.4 is a quadratic of the form Tm= K1ω2, where K1is a constant

2.4.3 Shaft power versus rotational speed

Variation of the shaft power P versus rotational speed ω is shown in Fig 2.5, for two wind speeds V and V, where V > V Now, the shaft power is

the product of shaft torque T and the shaft speed ω In S.I units, there is no

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constant of proportionality so that:

At zero speed, the shaft power is also zero, which is seen to be true for thetwo cases shown in Fig 2.5.4The shaft power also becomes zero when theshaft torque is zero, illustrated in the compatible diagrams of Figs 2.4 and

2.5 Maximum shaft power Pm increases with high values of wind speed.The locus of the maximum power points, shown as a dotted line in Fig 2.5,

is a cubic with the form Pm = K2ω3, where K2is constant The rotationalspeed at which maximum power is developed is not, in general, the same

as that for which maximum shaft torque occurs

2.4.4 Tip-speed ratio (TSR)

In order to express the power coefficient Cpin terms of both the upstream

wind velocity V and the blade rotational velocity ω, a parameter called

the tip-speed ratio (TSR) is defined Figure 2.6 illustrates the main physical

parameters, including the blade radius r The instantaneous velocity v of the blade tip is related to the angular velocity of rotation ω by the relationship:

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Fig 2.6 Motion of a two-blade propeller.1

The blade rotational velocity n in rpm is related to the angular velocity ω

in radians per second by the relationship:

ω= 2π n

If Cpis plotted against V , there will be a different characteristic for every value of ω Similarly, if Cp is plotted against ω, there will be a different characteristic for every value of V The characteristic of Cpversus TSR is a

“universal” curve that subsumes values of both ω and V Good rotor design requires that the maximum value of the power coefficient Cpmoccurs near

to the design-rated value of the rotational speed Typical characteristics forvarious different types of wind turbine are shown in Fig 2.7 The maximumideal efficiency characteristic for propeller machines is asymptotic to theBetz Law value of 0.593 It can be seen that the most efficient forms of

wind converter are the propeller type, for which 0.4 ≤ Cpm≤ 0.5 In

addi-tion, the maximum value of the power coefficient is designed to occur in

the range of TSR, namely 4 < TSR < 7 A more detailed performance

characteristic for propeller and Darrieus machines is shown in Fig 2.8 The

peak value of Cpis seen to be approaching 0.4, which is typical of smallwind converters

The power extractable from a freely flowing stream of wind, with a

power coefficient Cp = 0.4, is shown in Fig 2.9 using logarithmic scales

on both axes

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Fig 2.7 Power coefficient versus tip-speed ratio for various converters.

2.5 Mechanical Features of Wind Machines

2.5.1 Axial thrust (Pressure)

The action of the wind stream onto the rotating propeller, as in Fig 2.3, is

to create a pressure force acting along the horizontal shaft, called the thrust,

Th A detailed aerodynamic analysis (not given here) shows that the thrustmay be expressed as:

Axial Thrust= Th = 1

2ρAV

2 1

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Fig 2.8 Power coefficient versus tip-speed ratio for Darrieus and propeller machines.1

2.5.2 The “Yaw” effect

The wind at a given site is subject to rapid and frequent changes of direction.But to maintain efficient operation, the turbine propeller plane must remainperpendicular to the wind direction This requires that the turbine assembly

be free to rotate about a vertical axis—a phenomenon that aeronauticalengineers call the “yaw” effect With good bearings, a machine can bepivoted to swivel under the influence of a vane or a rudder wheel mounteddownwind, as illustrated in Fig 1.4 of Chap 1

In large modern wind turbines, a weather vane monitors the wind tion and an electric yaw drive is used to swivel the propeller plane broadsideonto the wind

direc-2.5.3 Gyroscopic forces and vibrations

Yawing rotation about the vertical axis while the rotor is turning about itshorizontal axis encounters strong gyroscopic forces These forces have to be

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Fig 2.9 Power extractable from a freely flowing wind stream (Cp= 0.4).1

transmitted through the bearings and propeller shaft causing high stressesand vibrations For this reason, the propeller blades of large machines aremade of a lightweight material such as a composite plastic such as fibreglassrather than metal

The action of rotation of the blades results in periodic vibrations With

a downwind-designed machine, which is characteristic of many large tems, each rotating blade passes through the wind shadow of the tower onceper rotation This results in a sudden reduction of air pressure on each bladefollowed by a sudden increase of air pressure, as it emerges from the shadow

sys-of the tower The result is to apply a bending moment on each blade at its

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root or hub joint in alternate directions Continual flexing of the propellerblades at every rotation produces fatigue stresses in the materials Withtwo-blade propellers, sometimes, the whole rotor is mounted on a single-shaft hinge allowing fore-aft rotation or “teetering” to reduce out-of-planebending moment fluctuations In order to minimise the vibration problem,some wind machine designers prefer to use three-blade propellers ratherthan two-blade propellers, even with the additional cost of the extra blade

2.5.4 Centrifugal forces

The rotation of the blades of a wind turbine causes outward acting centrifugalforces This phenomenon can be experienced by tying a weight at the end of

a string and swinging it around The outward acting force depends directly

on the mass or weight and on the speed of rotation Calculation of the trifugal forces on a wind turbine tending to pull the rotating propeller bladesout of their sockets is complicated because the weight is distributed non-uniformly along the length of the blade A simple calculation that assumedall the weight to be concentrated at a fixed radius of rotation would giveinaccurate results In large modern wind turbines, the blades are large andheavy Moreover, the cost of the blades and propeller unit is a significantportion of the total system cost

cen-The amount of power taken from the wind at a fixed wind velocity can beadjusted by varying the pitch angle of the propeller blades This is realised byrotating part of the propeller arms in their sockets, such as adjusting a screw

or bolt In effect, this changes the force and torque exerted on the rotatingpropeller The same principle is used in landing a propeller-driven aeroplane

to change the thrust on the blades and thereby reduce the speed The use ofthe same technique enables the power extracted from a propeller to be keptconstant over a range of wind speeds, illustrated in Fig 2.10 When the wind

reaches a maximum acceptable level known as the furling velocity Vf, thepitch angle of the blades can be adjusted so that zero power is extracted

In severe wind conditions, some form of mechanical brake is also applied

2.5.5 Solidity factor

The solidity factor is defined as the total blade area of the rotor divided bythe area swept normal to the wind In a horizontal axis, propeller machine,

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Fig 2.10 Effect of feathering the propeller.1V c = cut-in speed; V f = furling speed.

for example, an efficiently designed aerofoil intercepts a large area of windwith a small area of blade It therefore has a low-solidity factor, which ishighly desirable in high-rotational speed systems

Turbines with high-solidity factor usually suffer from a high degree ofaerodynamic interference between the blades, which results in low values

of TSR and power coefficient Cp Examples are the Savonius rotor and theAmerican farm multi-blade type, with the typical performance characteristicgiven in Fig 2.7 Wind turbines with high solidity usually operate at low-rotational speeds but have high-starting torques They are used for directmechanical applications such as water pumping but are not usually suitablefor driving electric generators For the purpose of electricity generation, it isusual to use low-solidity machines, such as the two-blade propeller, in order

to utilise high-operational speeds and high values of power coefficient

2.5.6 Two rotor blades or three rotor blades?

Most large modern wind turbines are horizontal axis, propeller machineshaving either two blades (in the USA) or three blades (in Europe) on therotor There are long-standing and ongoing differences of view amongstwind and aeronautical engineers as to the merits of the two designs The

maximum achievable values of power coefficient Cpover a range of values ofTSR have been calculated under the idealised condition of no aerodynamicdrag, for the rotors with several blade numbers

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Within the normal working range of TSR, a three-blade propeller has aslightly larger value (e.g., 5%) of power coefficient But most two-bladedwind turbines use a higher value of TSR than most three-bladed machines

There is little practical difference in the maximum achievable Cpbetweentwo- and three-bladed designs, assuming no drag

Three-blade machines have the advantage that the polar moment ofinertia with respect to yawing is constant, which contributes to smoothoperation A two-bladed rotor has a lower moment of inertia when theblades are vertical than when they are horizontal creating rotation imbal-ance An important consideration in selecting the number of blades is thatthe blade root stress increases with blade number for a turbine of given solid-ity In general, increasing the design TSR entails decreasing the number ofblades.5

2.5.7 Shaft torque and power

Most wind energy systems are used to generate electricity The wind turbine

is usually coupled to a generator directly as in Fig 2.11 (a) or via a gearbox

to step up the generator shaft speed, Fig 2.11 (b) For this reason, thegenerator is usually mounted at the top of the supporting tower along withthe gearbox Electric cables run down the tower to connect the generator toits electrical load on the ground below The torque, speed, and power of arotating shaft are linked by the relationship, given in Eq (2.27)

If the torque T is in newton-metres (Nm) and the angular speed of rotation ω is in radians per second then the power is in watts In Fig 2.11(b), the shaft torque into the gearbox Tt, from the turbine shaft, is given by:

Considerable torsional shear stress is imposed on a shaft due to rotational

forces For a solid cylindrical shaft subjected to a torque T , the torsional

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= wind turbine shaft speed

= generator shaft speed

(a)

(b) Fig 2.11 Power train for wind-powered electricity generation: (a) direct-on load, (b) gearbox system.1

stress fs, at any arbitrary radius rs, Fig 2.12, is given by:

fs = T · rs

J

N

where J is the polar (area) moment of inertia having the dimension (mass)4

or m4 For a solid cylindrical shaft of outer radius ro, the polar moment ofinertia can be shown to be:

J = π rO4m4

Combining Eqs (2.35) and (2.36) gives an expression for the shear stress

at the surface of a solid cylindrical shaft of radius ro:

fs= 2T

π r2N

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Fig 2.12 Wind machine shaft.1

2.6 Fixed Rotational Speed or Variable Rotational

Speed?

The ambient wind in any location is variable for both wind speed and tion In addition, a turbine is subject to turbulent wind gusts of a transientand unpredictable nature A design choice has to be made between operating

direc-a turbine direc-at vdirec-aridirec-able rotdirec-ationdirec-al speed following the wind direc-and reguldirec-ating thespeed of rotation to create a fixed speed or a choice of two (usually) differentfixed speeds of rotation For either option, the turbine must be capable ofbeing completely stalled into total immobility at some predetermined safemaximum operating speed

Any wind energy system design must aim to optimise the annual energycapture at its given site In order to operate at its highest efficiency (i.e., with

maximum power coefficient Cp), a turbine must operate at its optimum value

of TSR as the wind speed varies, as illustrated in Figs 2.7 and 2.8 The bestcondition to be aimed for in design is for the turbine to operate, at all windspeeds, at a value of TSR at or close to the value that results in maximumpower coefficient But since the wind speed varies the design issue is there-fore either (a) to operate the turbine rotor at a fixed speed by (say) adjustingthe pitch angle of the turbine propellers as the wind speed changes or (b) topermit the rotational speed to change, following the variable wind speed

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0 5 10 15

Wind speed [m/s]

Cut in Wind speed

Maximum rotor efficiency

Nominal power reduced rotor efficiency

No generation

Cut out Wind speed

Rated/Nominal Wind speed

Fig 2.13 Active power versus wind speed.6— pitch controlled; - stall controlled.

2.6.1 Constant speed operation

Operation at a constant speed may be realised by one of the two basic controlmethods:

1 by varying the pitch angle of the propeller blades as the wind speedvaries This can be achieved by rotating either the whole propeller blades

or the tips of the propeller blades in their sockets This form of control

is usually called pitch angle control

2 by the use of a propeller of fixed pitch angle but where the propellersurfaces are designed to introduce stall over a range of wind speeds.This form of design is usually referred to as “stall regulation” or “stallcontrol”

The two design methods lead to very similar turbine power characteristics,

as shown in Fig 2.13 At low wind speeds (1–3 m/s), the turbines are shutdown Start-up begins at a cut-in speed between 2.5 and 5 m/s Rated windspeed, at which the nominal output is reached, is in the range of 12–15 m/s.Below the nominal wind speed, the aim is to maximise the turbine rotorefficiency.6

When the turbine rotational speed is constant, a coupled A.C generatorwill operate at a fixed frequency, which can be synchronised to the frequency

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